Modelling and FEM simulation of electric field assisted sintering of tungsten carbide (WC)

Transcription

1 Engineering Conferences International ECI Digital Archives Electric Field Assisted Sintering and Related Phenomena Far From Equilibrium Proceedings Winter Modelling and FEM simulation of electric field assisted sintering of tungsten carbide (WC) Sree Koundinya Follow this and additional works at: Part of the Engineering Commons Recommended Citation [1] M. Abouaf, J. Chenot, G. Raisson and P. Bauduin, "Finite element simulation of Hot isostatic pressing of metal powders," International Journal of Numerical Methods Engineering, Vol.25, pp , [2] H. Riedel and B. Blug, "A comprehensive model for solid state sintering and its application to silicon carbide," in Multiscale Deformation and Fracture in Materials and Structures, Springer Netherlands, pp. 49-7,22. [3] T. Kraft and H. Riedel, "Numerical simulation of solid state sintering; model and application," Journal of the European Ceramic Society, vol. 24, no. 2, pp , 24. [4] Z. Shen, M. Johnsson, Z. Zhao and M. Nygren, "Spark Plasma Sintering of Alumina.," Journal of the American Ceramic Society, no. 85, p , 22. [5] Y. Song, Y. Li, Z. Zhau, Y. Lai and Y. Ye, "A multi-field coupled FEM model for one-step-forming process of spark plasma sintering considering local densification of powder material," Journal of materials science, vol. 46, no. 17, pp , 211. This Abstract and Presentation is brought to you for free and open access by the Proceedings at ECI Digital Archives. It has been accepted for inclusion in Electric Field Assisted Sintering and Related Phenomena Far From Equilibrium by an authorized administrator of ECI Digital Archives. For more information, please contact

2 Modelling and FEM Simulation of Electric Field Assisted Sintering of Tungsten Carbide (WC) S.K.Sistla, M.Hajeck, A.Kaletsch, C.Broeckmann Institute for Materials Applications of Mechanical Engineering Electric Field Assisted Sintering and Related Phenomena Far from Equilibrium, ECI Conference, Tomar(Portugal),

3 Previous Work Cylindrical Sample Bi Layer Laminate Sample 2 [C. van Nguyen, S.K. Sistla et.al Japanese Ceramic Society 216]

4 Outline Introduction Motivation Objectives Research Hypothesis Modelling Field Assisted Sintering (FAST) Modeling densification Material parameters Results SPS Experiments with WC Coupled structural thermal electrical simulation Conclusion 3 Outlook

5 Introduction Motivation FAST is an emerging powder consolidation technique Limited numerical investigations of FAST Complex material transport mechanisms Objectives Model the densification behavior from existing FAST models. Model inelastic strain components for building a material model Correlate the experimental behavior with the numerical simulations Research Hypothesis Selection of a conducting material (here binder less WC) SPS Experiments to determine the boundary conditions Build coupled structural thermal electrical simulations Verify the simulation results such as densification 4

6 Outline Introduction Motivation Objectives Research Hypothesis Modelling Field Assisted Sintering (FAST) Modeling densification Material parameters Results SPS Experiments with WC Coupled structural thermal electrical simulation Conclusion 5 Outlook

7 Modelling Field Assisted Sintering Modelling densification ε ij = ε el inel ij + ε ij ε inel ij = ε cr sw ij + ε ij 1 2 Constitutive Model for FAST of Conductive Materials [1] ε = ε gb + ε cr 3 Total Strain rate due to grain boundary diffusion ε gb = ε em gb + ε st dl gb + ε gb 4 Strain rate component due to electro migration ε em gb = δ gbd gb kt Z e q U 2 2r+r p l 5 Strain rate component due to sintering stress ε st gb = δ gbd gb kt Ω 2 3α 2r+r p 2r 1 r p 1 4r 6 Strain rate component due to external load ε dl gb = δ gbd gb kt Ω 2r+r p σ z 4r [1-Olevsky 26]

8 Modelling Field Assisted Sintering Modelling densification Based on the continuum theory of sintering [2] σ z = A 1 W m 1 φ ε crz + ψ 1 φ ( ε 3 crr + ε crz ) + σ s 8 Since, WC is a single phase material m = 1 and from boundary conditions ε crr = Total Strain rate due to Power law creep ε crz = σ z+ σ kk 3 σ s φ = ρ 2, ψ = 2 3 A 1 ψ+ 2 3 φ 9 ρ 3 (1 ρ), σ s = 3α 2r ρ2 1 With conservation of mass ρ = ρ ε kk 11 7 [2-Olevsky 1998]

9 Modelling Field Assisted Sintering Material parameters Material Material Property Value Literature Tungsten Carbide (WC) Density 1525 kg/m 3 [3] E-Modulus 6 GPa [3] Poisson's Ratio.3 [3] Thermal Conductivity 28 W/m.K [3] Specific Heat 292 J/kg.K [3] Electrical Conductivity 2.39 S/m [3] Graphite Density 185 kg/m 3 [4] E-Modulus 2 GPa [4] Poisson's Ratio.3 [4] Thermal Conductivity x1-2 T W/m.K [4] Specific Heat xT J/kg.K [4] Electrical Conductivity 1/(26-3x1 2 T+2x1-5 T 2-6.4x1-9 T x1-13 T 4 )x1 6 S/m [4] 8 [3- [4-Song 211]

10 Modelling Field Assisted Sintering Model parameters Material Material Property Value Tungsten Carbide (WC) Initial Relative Density.8259 Initial grain size 3 µm Equivalent Charge e-18 C Atomic Volume 1.294e-29 m 3 Surface Tension 1.12 J/m 2 Grain-boundary diffusion frequency factor 5e-1m 3 /s Activation energy for grain-boundary diffusion J/mol Activation energy for power-law creep 591 J/mol Power-law creep frequency factor 261 MPa/s Electrical Field per Unit length 9 V/m 9

11 Modelling Field Assisted Sintering Implementation of densification model Densification Model (User Subroutine CREEP) Part Geometry (ABAQUS CAE) Coupled Structural Thermal Electrical Model ABAQUS Standard Initial Conditions Temperature, Interactions Boundary Conditions Voltage, Pressure Post Processing (ABAQUS ODB) Relative density, Volumetric Changes, Stresses, etc. 1

12 Outline Introduction Motivation Objectives Research Hypothesis Modelling Field Assisted Sintering (FAST) Modeling densification Material parameters Results SPS Experiments with WC Coupled structural thermal electrical simulation Conclusion 11 Outlook

13 Pressure [MPa] Voltage [V] Temperature[ C] Punch Displacement [mm] Results SPS Experiments at 19 C Heating Rate 2 K/min Holding Time 2 min , ,5 2 1,5 1, Time [s] Time [s] Results as input for FEM Simulations Results for verification of FEM Simulations 12

14 Pressure [MPa] Voltage [V] Temperature[ C] Punch Displacement [mm] Results SPS Experiments at 2 C Heating Rate 2 K/min Holding Time 2 min ,5 2 1,5 1, Time [s] Time [s] Results as input for FEM Simulations Results for verification of FEM Simulations 13

15 Results Model parameters 14 Symmetric Model

16 Temperature [ C] Punch Displacement [mm] Results SPS Experiments at 19 C Heating Rate 2 K/min Holding Time 2 min 2 1, Experiment Simulation,8,6,4,2 Experiment Simulation Time [s] Time [s] Results as input for FEM Simulations Results for verification of FEM Simulations 15

17 Results SPS Experiments at 19 C Heating Rate 2 K/min Holding Time 2 min Relative Density Evolution 16

18 Temperature[ C] Punch Displacement [mm] Results SPS Experiments at 2 C Heating Rate 2 K/min Holding Time 2 min 25 1, Experiment Simulation,8,6,4,2 Experiment Simulation Time [s] Time [s] Results as input for FEM Simulations Results for verification of FEM Simulations 17

19 Temperature [ C] Punch Displacement [mm] Results Sensitivity Analysis SPS Experiments at 19 C 25 1, Experiment Simulation_L1,8,6,4 Experiment Simulation_L1 5 Simulation_L2,2 Simulation_L Time [s] Time [s] 18

20 Temperature[ C] Punch Displacement [mm] Results Sensitivity Analysis SPS Experiments at 2 C 25 1, Experiment Simulation_L1,8,6,4 Experiment Simulation_L1 5 Simulation_L2,2 Simulation_L Time [s] Time [s] 19

21 Outline Introduction Motivation Objectives Research Hypothesis Modelling Field Assisted Sintering (FAST) Modeling densification Material parameters Results SPS Experiments with WC Coupled structural thermal electrical simulation Conclusion 2 Outlook

22 Conclusion Mass transport mechanisms for FAST can be investigated and analyzed with coupled structural, thermal and electrical FEM simulations in a single step. Electrical field influences densification for conducting materials. Coupled electrical thermal simulations gives an insight into accurate prediction of the temperature gradient in the powder and computational time is shorter. 21

23 Outline Introduction Motivation Objectives Research Hypothesis Modelling Field Assisted Sintering (FAST) Modeling densification Material parameters Results SPS Experiments with WC Coupled structural thermal electrical simulation Conclusion 22 Outlook

24 Outlook Material properties for the powder and the tools dependent on relative density and temperature need to be experimentally determined for more accurate FAST simulations Further numerical investigations need to be carried out to reduce the non-convergence caused due to nonlinearity in material modelling and contacts(thermal, mechanical and structural). Model parameters need to be accurately estimated for effective estimation of densification and volumetric changes. With more experiments and material characterization a better understanding and modifications would be proposed to the existing constitutive equation for densification by FAST 23

25 We appreciate the help of Global Tungsten & Powders for supply of WC powder! Thank you for your kind attention! Sree Koundinya Sistla IWM Institute for Materials Applications in Mechanical Engineering RWTH Aachen University Augustinerbach Aachen